Research map / Optimization / Nonconvex and smooth optimization
Stochastic Cubic Regularization for Fast Nonconvex Optimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use stochastic cubic regularization with stochastic gradients and Hessian-vector products instead of SGD | Stochastic nonconvex optimization · Stochastic nonconvex optimization | oracle evaluations to find approximate local minimum: $\mathcal{O}(\epsilon^{-4} \text{poly}(d))$ -> $ \mathcal{\tilde{O}}(\epsilon^{-3.5})$ | Helped |
| Use stochastic cubic regularization without variance reduction rather than a variance-reduction method | Stochastic nonconvex optimization · Stochastic nonconvex optimization | oracle evaluations to find approximate local minimum: $\mathcal{\tilde{O}}(\epsilon^{-3.5})$ | No clear effect |
| Use stochastic cubic regularization rather than SGD | Synthetic nonconvex problem · Synthetic nonconvex problem | objective value versus oracle calls | Helped |
| Use stochastic cubic regularization rather than SGD or AdaGrad | Deep autoencoder · MNIST deep autoencoding task | training error | Helped |
| Use stochastic cubic regularization rather than AdaGrad after reaching a local-optimum basin | Deep autoencoder · MNIST deep autoencoding task | training error | Hurt |
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